Least Common Multiple (LCM) of 189 and 82
The least common multiple (LCM) of 189 and 82 is 15498.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 189 and 82?
First, calculate the GCD of 189 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 82 = 2 remainder 25 |
| 2 | 82 ÷ 25 = 3 remainder 7 |
| 3 | 25 ÷ 7 = 3 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 184 | 20056 |
| 157 and 84 | 13188 |
| 171 and 189 | 3591 |
| 152 and 184 | 3496 |
| 112 and 112 | 112 |